几乎完全非线性多项式函数间的EA等价性

简述了几乎完全非线性(APN)多项式函数的研究现状,讨论了两类几乎完全非线性多项式函数间的扩张仿射(EA)等价性,给出了验证EA等价的一般方法.     

用改进的凝聚约束同伦方法求解一类Brouwer不动点问题

In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65), the main adavantages of this method are as follows: on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in Rn (in this paper, we let Ω = [x ∈ Rn: gi(x) ≤ 0, i = 1,… ,m]); on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively.     

关于局部随机吸引子若干性质的注记(英文)

In this note, we study some properties of local random pull-back attractors on compact metric spaces. We obtain some relations between attractors and their fundamental neighborhoods and basins of attraction. We also obtain some properties of omega-limit sets, as well as connectedness of random attractors. A simple deterministic example is given to illustrate some confusing problems.     

求解一类非线性规划的连续同伦方法(英文)

In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is effective. It should be pointed out that we extend the results of Lin et al. （see Appl. Math. Comput., 80（1996）, 209-224） to a broader class of non-convex programming problems.     

内点同伦方法求解更一般非凸集上的不动点问题(英文)

In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence of fixed points,which can lead to an implementable globally convergent algorithm.     

Solving a Class of Brouwer Fixed-point Problems via a Modified Aggregate Constraint Homotopy Method

In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method （proposed by Yu and Lin, Appl. Math. Comput., 74（1996）, 65）, the main adavantages of this method are as foUows： on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in R^n （in this paper, we let Ω={x∈ R^n ： gi（x） ≤0, i= 1,... , m}）; on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively.     

连续化方法求解一般无界非凸规划的K-K-T点

给出了求解无界非凸规划的K-K-T系统的一种连续化方法,在适当的条件下,得到了连接可行域内部任意给定的点和非凸规划的K-K-T点的同伦路径存在性的构造性证明,从而构建了可数值实现的全局收敛性算法.数值算例进一步验证了本文结果的有效性.     

求解Brouwer不动点问题的改进同伦方法

In this paper,we modify the homotopy method(proposed by Yu and Lin,Appl.Math.Comput.,74(1996),65)and hence make the modified method be able to solve Brouwer fixed-point problems in a broader class of nonconvex subsets in R~n.In addition,a simple example is given to show the effectiveness of the modified method.